Computational Aspects of Realization & Design Algorithms in Linear Systems Theory.
Realization and design problems are two major problems in linear time-invariant systems control theory and have been solved theoretically. However, little is understood about their numerical properties. Due to the large scale of the problem and the finite precision of computer computation, it is very important and is the purpose of this study to investigate the computational reliability and efficiency of the algorithms for these two problems. In this dissertation, a reliable algorithm to achieve canonical form realization via Hankel matrix is developed. A comparative study of three general realization algorithms, for both numerical reliability and efficiency, shows that the proposed algorithm (via Hankel matrix) is the most preferable one among the three. The design problems, such as the state feedback design for pole placement, the state observer design, and the low order single and multi-functional observer design, have been solved by using canonical form systems matrices. In this dissertation, a set of algorithms for solving these three design problems is developed and analysed. These algorithms are based on Hessenberg form systems matrices which are numerically more reliable to compute than the canonical form systems matrices.
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- Physics: Electricity and Magnetism